= Solution
Nonrelativistic acceleration from rest gives $p=\sqrt{2m_eeV}$ and $\lambda=h/p$. The observed deflection is the angle between incident and diffracted beams, \b[$2\theta=22^\circ$], so <Bragg's law> at first order gives
$$
\boxed{d=\frac{h}{2\sin11^\circ\sqrt{2m_ee(150\,\mathrm V)}}\simeq2.62\times10^{-10}\,\mathrm m=0.262\,\mathrm{nm}.}
$$
Here $\lambda\simeq0.100\,\mathrm{nm}$. The numerical evaluation uses the externally documented CODATA 2014 values $h=6.626070040\times10^{-34}\,\mathrm{J\,s}$, $m_e=9.10938356\times10^{-31}\,\mathrm{kg}$ and $e=1.6021766208\times10^{-19}\,\mathrm C$; it does not assert which rounded constants were in the exam's handbook. Relativistic corrections at this voltage are negligible at the precision of the angle.<CODATA recommended values of the fundamental physical constants 2014 by National Institute of Standards and Technology>[Planck constant, elementary charge and electron mass in the historical reference table]{ref}
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